K013 $K_L \to \pi^0\gamma\gamma$

This is not a clean tree-level KK-gluon constraint like \(\varepsilon_K\) or \(\Delta m_K\). It is a \(\Delta S=1\) radiative rare decay dominated by long-distance chiral dynamics and vector-meson-exchange effects. Its practical catalog role is diagnostic: it fixes the size and shape of the two-photon amplitude that feeds the CP-conserving part of \(K_L\to\pi^0\ell^+\ell^-\), and it checks whether an RS extension with enhanced \(s\to d\gamma\gamma\), dipole, or electroweak-penguin structure is already in tension with radiative kaon data.

Relative to the Csaki--Falkowski--Weiler era, the KTeV full-sample analysis is the decisive update: it superseded the earlier KTeV value and is one of the two inputs in the current PDG average. The author did not find a newer neutral-mode branching-ratio measurement in the PDG 2025 listing. The main later experimental development is adjacent rather than identical: NA48/2 measured the charged analogue \(K^\pm\to\pi^\pm\gamma\gamma\), with the sidecar recording the model-independent \(z>0.2\) and ChPT-extrapolated branching fractions. Cappiello, Cata, and D'Ambrosio 2018 show that radiative-kaon data constrain weak chiral counterterms, which is the right language for this mode rather than a short-distance Wilson-only bound.

Class: long-distance-limited and model-dependent. The measured branching fraction should not be imposed as a hard RS exclusion without a dedicated \(\Delta S=1\) radiative calculation and a prescription for the SM long-distance amplitude. It is safer as a consistency target and as an auxiliary input to \(K_L\to\pi^0\ell^+\ell^-\) estimates. A new-physics interpretation must avoid double counting two-photon contributions already absorbed into chiral counterterms.

NO. The author reran the plan-required greps and a K013-specific search across quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/. The repository contains kaon \(\Delta F=2\) machinery and unrelated generic \(\gamma\)-symbol occurrences, but no implementation of \(K_L\to\pi^0\gamma\gamma\), no \(a_V\) parameter, and no radiative-kaon likelihood.

HIGH. A production constraint would need new \(\Delta S=1\) radiative matching, chiral-amplitude inputs, long-distance SM treatment, and possibly differential-shape information. The existing \(\Delta F=2\) operator basis and running code are not enough.

Process-local source keys before bibliography consolidation: PDG2025\_KL\_pi0gammagamma, KTeV2008\_KL\_pi0gammagamma, NA482002\_KL\_pi0gammagamma, NA482014\_Kpm\_pigammagamma, CappielloCataDAmbrosio2018\_radiative\_chiral, and GabbianiValencia2001\_KL\_pi0gammagamma.